A few months ago I watched a great PBS special on String Theory hosted by "The Elegant Universe" author Brian Greene and was very impressed with the show. Physicists at the University of Washington say the universe favors 3 or "7" dimensions.
"That's what comes out when you do the math," said Andreas Karch, a University of Washington assistant professor of physics. The article goes on to say, "...the way our universe started and then diluted as it expanded -- what they call the relaxation principle -- favored formation of three- and seven-dimensional realities."
Wow, I guess God flipped a coin on that one and here we are in 3-D! (That is if you believe in that sort of thing!)